Algebraic invariants of singularities

奇点的代数不变量

• 批准号: DP170102328
• 负责人: Prof Christian Haesemeyer
• 金额: $ 24.14万
• 依托单位: The University of Melbourne
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2017
• 资助国家: 澳大利亚
• 起止时间: 2017-01-15 至 2022-12-31
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP170102328
• 关键词: Algebraic; invariants; singularities

This project aims to study the local and global behaviour of singularities that algebraic equations can describe via difficult algebraic invariants constructed from (algebraic) functions on the geometric object. A geometric object has a singularity at a point where its tangent directions do not behave the way they should. Examples include black holes, the vertex of a cone or a road intersection. This project is expected to contribute to fundamental research goals in pure mathematics, and increase the international competitiveness of Australian mathematics research.

该项目旨在研究奇异点的局部和全局行为，代数方程可以通过从几何对象上的（代数）函数构造的困难代数不变量来描述。一个几何对象在一个点上有一个奇点，在这个点上，它的切线方向的行为并不像它们应该的那样。例子包括黑洞，圆锥体的顶点或道路交叉口。该项目预计将有助于实现纯数学的基础研究目标，并提高澳大利亚数学研究的国际竞争力。